Question

An air freshener starts with 44 grams and evaporates. In each of the following cases, write a formula for the quantity, Q grams, of air freshener remaining t days after the start.

(a) The decrease is 4 grams per day. Q(t) =
(b) The decrease is 15% per day.
(c) The decrease is at a continuous rate of 8% per day. Q(t) =

Answer 1

The formula for the remaining quantity of air freshener depends on the rate of decrease per day. For a decrease of 4 grams per day, the formula is Q(t) = 44 - 4t. For a decrease of 15% per day, the formula is Q(t) = 44 * (1 - 0.15)^t. For a decrease of 8% per day, the formula is Q(t) = 44 * e^(-0.08t).

Step-by-step explanation:

(a) The decrease is 4 grams per day. The formula for the quantity of air freshener, Q grams, remaining t days after the start is Q(t) = 44 - 4t.

(b) The decrease is 15% per day. The formula for the quantity of air freshener, Q grams, remaining t days after the start is Q(t) = 44 * (1 - 0.15)^t.

(c) The decrease is at a continuous rate of 8% per day. The formula for the quantity of air freshener, Q grams, remaining t days after the start is Q(t) = 44 * e^(-0.08t), where e is the base of the natural logarithm.